Let's say my name was John. If I traveled to Mexico and introduced myself to a native as John,
"Hola, me llamo John."
Would they refer to me as John... or would they immediately translate my name into the Spanish equivalent, Juan?

A classmate of mine informed me that if he were to go to Mexico and introduce himself as James, a native would immediately refer to him as Jaime. This struck me as odd. Why would someone call me Juan if I told them my name was John?